A curve f(x,y) is defined by sin(3y)+3ye^(-2x)+2x^2 = 5. Find dy/dx
In questions where we have a function of x and y equal to a constant, we need to find dy/dx indirectly.We use the formula (df/dx) + (df/dy)(dy/dx) = 0So all we do is differentiate each term in the function with respect to x (assuming y is a constant) to give us our df/dx term, which is 0-6ye-2x+4x.Then we differentiate each term with respect to y (now assuming x is a constant) to give us our df/dy term, which is 3cos(3y)+3e2x+0.Plugging these terms directly into our formula and re-arranging for dy/dx we get:dy/dx = (6ye-2x-4x)/(3cos(3y)+3e-2x)
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